The yield stress of a polymer is measured to be 20 MPa at a temperature of 300 K and a strain r

step 1 So what I have on the screen here is the Uranus equation for two different temperatures. This is

The yield stress of a polymer is measured to be 20 MPa at a...

The yield stress of a polymer is measured to be $20 \mathrm{MPa}$ at a temperature of $300 \mathrm{~K}$ and a strain rate of $10^{-3} \mathrm{~s}^{-1}$. When the strain rate is doubled from this value, the yield stress is observed to increase by $10 \%$. What is the apparent activation volume for yield in this case?

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Key Concepts

Activation Volume

Activation volume is a macroscopic parameter that represents the effective volume associated with the molecular rearrangements or transitions occurring during yielding. It quantifies how sensitive the yield stress is to changes in the strain rate and temperature, reflecting the size of the region involved in the deformation process.

Strain Rate Sensitivity

Strain rate sensitivity describes how the stress at which yielding occurs changes as the rate of deformation increases. In many polymers and other materials, the yield stress increases with an increasing strain rate, and this dependence is often modeled logarithmically. The relationship between stress and the logarithm of the strain rate is key to extracting the activation volume.

Thermally Activated Process

Yielding in polymers is often considered a thermally activated process, meaning that the molecular events that lead to deformation overcome an energy barrier. This behavior is captured by Arrhenius-type equations where thermal energy (characterized by kT) competes with the mechanical work, linking temperature, strain rate, and yield stress. The activation volume appears in these expressions by scaling the effect of thermal fluctuations on the rate-dependent yield stress behavior.

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